Abstract

Some results of this paper were presented at the VII-th Autumn Logical School held by the Section of Logic Polish Academy of Sciences, Podklasztorze , 16-25 November, 1983. A Nelson algebra is an algebra of the type which satisfies some appropriate axioms . These axioms imply that the relation ≈ on A defined by: a ≈ b if and only if a → b = 1 and b → a = 1, is a congruence relation on , and the quotient algebra Ah = / ≈ is a Heyting algebra. For a given Heyting algebra B there always exists a Nelson algebra A such that Ah is isomorphic to B: the Fidel-Vakarelov construction of the Nelson algebra N yields an example of such an algebra. In this paper we describe all Nelson algebras A whose Ah ’s are isomorphic to a given Heyting algebra B; and next we consider some problems, related with this description, concerning equational and quasiequational subclasses of the class N of all Nelson algebras. Our description is obtained by an application of the topological duality theory of Priestley for bounded distributive lattices